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- W4297201833 abstract "We obtain an upper bound on the minimal number of points in an $epsilon$-chain joining two points in a metric space. This generalizes a bound due to Hambly and Kumagai (1999) for the case of resistance metric on certain self-similar fractals. As an application, we deduce a condition on $epsilon$-chains introduced by Grigor'yan and Telcs (2012). This allows us to obtain sharp bounds on the heat kernel for spaces satisfying the parabolic Harnack inequality without assuming further conditions on the metric. A snowflake transform on the Euclidean space shows that our bound is sharp." @default.
- W4297201833 created "2022-09-27" @default.
- W4297201833 creator A5013672554 @default.
- W4297201833 date "2019-09-22" @default.
- W4297201833 modified "2023-09-28" @default.
- W4297201833 title "On the length of chains in a metric space" @default.
- W4297201833 doi "https://doi.org/10.48550/arxiv.1909.09988" @default.
- W4297201833 hasPublicationYear "2019" @default.
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